# Zeno2 - Zeno Argument against Plurality 1 Introduction The...

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Zeno: Argument against Plurality 1. Introduction The argument is contained in 4 =B1 and 3 =B2 (from Simplicius’ commentary on Aristotle’s Physics ). But there is a problem with the text, and some of the argument is garbled or lost. Fortunately, we can reconstruct it. Zeno attempts to show that the assumption that there are many things leads to a contradiction: viz., that each thing is both infinitely small and infinitely large. There are two limbs to the argument. The pluralist’s assumption, “There are many things,” leads to these two conclusions: A. Each thing is “so small as not to have size.” B. Each thing is “so large as to be unlimited.” Simplicius’s text does not preserve (A) completely. It starts with (A), and then is garbled and switches over to (B). But we can reconstruct the argument for (B). 2. The Argument Simplicius (in 4 =B1) preserves one key principle (“if it exists, each thing must have some size and thickness”). It is a premise that Zeno thinks his materialist/pluralist opponents must accept. 3 =B2 contains an argument in support of this principle (“Suppose that x has no size. Then when x is added to a thing it does not increase the size of that thing, and when x is subtracted from a thing, that thing does not decrease in size. Clearly, x is nothing, i.e., does not exist.”). So the argument begins with this premise: A. What exists has size (magnitude). Zeno also seems to be making the following two assumtions:

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Zeno2 - Zeno Argument against Plurality 1 Introduction The...

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